Analysis of previous microscopic calculations for the second 0 + state in 12 C in terms of 3-α particle Bose-condensed state

The wave function of the second ${0}^{+}$ state of ${}^{12}\mathrm{C},$ which was obtained a long time ago by solving the microscopic $3\ensuremath{\alpha}$ problem, is shown to be almost completely equivalent to the wave function of the $3\ensuremath{\alpha}$ condensed state, which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second ${0}^{+}$ state of ${}^{12}\mathrm{C},$ which is the key state for the synthesis of ${}^{12}\mathrm{C}$ in stars (``Hoyle'' state), and which is one of the typical mysterious ${0}^{+}$ states in light nuclei, as a gaslike structure of three $\ensuremath{\alpha}$ particles, Bose condensed into an identical s-wave function.